Ben is 20 years older than Luis. Nineteen years ago, Ben was 3 times as old as Luis. How old is Luis now?
Answer: We can use the given information to write down two equations that describe the ages of Ben and Luis. Let Ben's current age be $b$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $b = l + 20$ Nineteen years ago, Ben was $b - 19$ years old, and Luis was $l - 19$ years old. The information in the second sentence can be expressed in the following equation: $b - 19 = 3(l - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: $b = l + 20$ . Substituting this into our second equation, we get the equation: $(l + 20)$ $-$ $19 = 3(l - 19)$ which combines the information about $l$ from both of our original equations. Simplifying both sides of this equation, we get: $l + 1 = 3 l - 57$ Solving for $l$ , we get: $2 l = 58$ $l = 29$.